This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128465 #16 Feb 16 2025 08:33:04
%S A128465 1,5,7,71,379,2659
%N A128465 Numbers k such that k divides the numerator of alternating Harmonic number H'((k+1)/2) = A058313((k+1)/2).
%C A128465 For k > 1 all 5 listed terms are primes.
%C A128465 The only known numbers k such that k divides the numerator of alternating Harmonic number H'((k-1)/2) = A058313((k-1)/2) are the Wieferich primes (A001220): 1093 and 3511.
%C A128465 An odd prime p = prime(n) belongs to this sequence iff Fermat quotient A007663(n) == A130912(n) == 2*(-1)^((p+1)/2) (mod p). - _Max Alekseyev_, Nov 30 2022
%H A128465 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%t A128465 f=0; Do[ f = f + (-1)^(n+1)*1/n; g = Numerator[f]; If[ IntegerQ[ g/(2n-1) ], Print[2n-1]], {n,1,3000} ]
%Y A128465 Cf. A001008, A007663, A001220, A058313, A125854, A121999, A130912.
%K A128465 hard,more,nonn
%O A128465 1,2
%A A128465 _Alexander Adamchuk_, Mar 10 2007
%E A128465 Edited by _Max Alekseyev_, Nov 30 2022